Packet and chart conventions

Work first in dimensionless transverse spacetime coordinates $y=(\tau ,X,Y)$ with ${\eta }_3=\mathrm{diag}(-1,1,1)$. Let $t=(1,0,0{)}^{\mathsf{T}}$ and

Its product lift fixes $\zeta$. We use the same notation for that lift.

Allowed reference-frame changes are proper time-oriented Lorentz-affine transformations in the transverse spacetime, extended by the identity on the axial factor. For $A=(L,a_0)$, define

The packet records the defect identifier, deficit, frame, worldsheet, rest vector, and full affine map.